Carnot Efficiency Calculator
Fast, accurate, and free online Carnot Efficiency Calculator tool that runs directly in your browser.
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Enter the source and cooler temperatures
Enter the temperature values $T_h$ and $T_c$ (remembering that the source temperature must be higher than the cooler temperature) and click the calculation button.
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Other tools you may find usefulCarnot engine calculator - ideal efficiency and heat balance
The tool calculates the parameters of an ideal Carnot heat engine operating between two heat reservoirs: a hot one atThand cool in temperatureTc. You will appointefficiency η = 1 - Tc/Th, as well as the energy suppliedQin, useful workWand energy transferred to a cold sourceQout. The interface should provide fieldsTh, Tc, Qinand unit selectorT_unit= K or C as wellprecisionfor formatting results.
Patterns and theory
Ideal efficiency of the Carnot engine
η = 1 - Tc / Th
WhereThis the absolute temperature of the hot source [K], aTcabsolute temperature of the cold source [K]. For data in °C, the calculator should convert to kelvin byT[K] = t[°C] + 273.15.
Energy and work relationships
Useful work
W = η Qin
Heat transferred to a cool source
Qout = Qin - W = Qin · (1 - η) = Qin · Tc/Th
Why Carnot sets the limit
The Carnot cycle consists of two isothermal and two adiabatic reversible transformations. It is the efficiency benchmark for any engine operating between the same temperatures. No actual heat engine can exceed the valueηdetermined by the Carnot formula due to irreversibility, flow losses and friction.
Model assumptions
- Reversible transformations and no mechanical losses.
- TemperaturesTh i Tcare constant during heat exchanges.
- No limits on process speeds and heat losses to the environment.
- Work is calculated in energy units [J, kJ], heat in the same units.
Form fields and units
- Th- hot source temperature [K or °C, controlledT_unit]
- Tc- temperature of the cold source [K or °C].
- Qin- heat input in the cycle [J, kJ].
- precision- number of decimal places in the results.
- W, Qoutandηare calculated automatically after entering the data.
| Size | Symbol | Units | Comments |
|---|---|---|---|
| Temperature hot | Th | K, °C | Use K in calculations |
| Cool temperature | Tc | K, °C | Use K in calculations |
| Efficiency | η | - | 0 ≤ η < 1 |
| Heat supplied | Qin | J, kJ | Energies on the same scale |
| Useful work | W | J, kJ | W = η·Qin |
| Warmth given | Qout | J, kJ | Qout = Qin - W |
Calculation examples
Example 1 - efficiency from temperatures
- Th = 600K
- Tc = 300 K
- Qin = 500 kJ
η = 1 - 300/600 = 0.5. W = 0.5 · 500 = 250 kJ. Quout = 500 - 250 = 250 kJ. An engine operating between 600 K and 300 K will, at best, convert half of the heat energy into work.
Example 2 - data in °C
- Th = 500 °C → 773.15 K
- Tc = 30 °C → 303.15 K
- Qin = 1.2 MJ
η = 1 - 303.15/773.15 ≈ 0.6079. W ≈ 0.6079 · 1.2 MJ ≈ 0.729 MJ. Qout ≈ 0.471 MJ. Converting to kelvins is key - use absolute temperatures.
Example 3 - cooler source
- Th = 650 K
- Tc = 280 K
- Qin = 800 kJ
η = 1 - 280/650 ≈ 0.5692. W ≈ 455.4 kJ. Qout ≈ 344.6 kJ. The lower Tc relative to Th, the higher the theoretical efficiency.
Example 4 - limit at temperatures close to
- Th = 350 K
- Tc = 320 K
- Qin = 400 kJ
η = 1 - 320/350 ≈ 0.0857. W ≈ 34.3 kJ. Qout ≈ 365.7 kJ. A small temperature difference results in low efficiency - in practice, additional losses will reduce it even more.
Engineering scenarios
| Application | Data | Assumptions | Key result |
|---|---|---|---|
| Turbine technology comparison | Th exhaust gas, Tc cooling | Theoretical limit | Carnot η as maximum |
| Steam cycle analysis | Saturated steam and condenser temperature | Actual efficiency lower | Heat transfer improvement required |
| Cooling design | Tc, Th ranges | Cooler and medium selection | Influence of Tc on possible operation |
| Assessment of renewable energy potential | Th storage tank, Tc ambient | Ideal cycle | Realistic profit prediction |
How to use the calculator
- Select temperature unitT_unit- K or °C. If you are working in °C, the calculator will convert to K.
- EnterTh i Tc. Make sure Th > Tc.
- EnterQinin J or kJ. Energy units must be consistent for all results.
- Setprecisionfor number presentation.
- Readη, W i Qoutin the results panel.
Common pitfalls and good practices
- Temperatures in K- the η formula uses kelvins. Never substitute °C without conversion.
- Th must be greater than Tc- otherwise the result η will be negative or nonsense.
- Limit values - for Tc approaching absolute zero, η approaches 1, which is not achievable in practice.
- Actual losses- friction, irreversibility, pressure differences and conduction through the walls reduce the efficiency compared to Carnot.
- Energy Coherence- if you report Qin in kJ, present W and Qout in kJ for clarity.
Extensions - refrigerator and Carnot heat pump
Refrigerator efficiency coefficient
COP_R = Tc / (Th - Tc)
Determines how much heatQoutcan be received from the cold source per unit of workW.
Pump efficiency coefficient heat
COP_HP = Th / (Th - Tc)
Determines how much heatQinwill go to the hot source per unit of workW. In HVAC applications, important for assessing efficiency.
Although this calculator focuses on engine operation, these formulas allow you to quickly convert parameters when you reverse the direction of circulation.
FAQ
Can I give temperatures in °C
Yes, but the calculator must convert them to kelvins. Efficiency η = 1 - Tc/Th only works for K.
Why is the efficiency result negative
This usually means that Tc is greater than or equal to Th, or temperatures are given in °C without conversion to K.
Is Carnot efficiency achievable
No. This is a theoretical limit. The actual efficiency is lower due to irreversibility and losses.
What is the maximum work from a given amount of heat
The maximum is determined by W = η · Qin. Choose high Th and low Tc, but remember material and economic constraints.
What energy units are supported
J and kJ. It is important that all energy quantities are consistent. 1 kJ = 1000 J.
Summary
The Carnot engine calculator determines the theoretical maximum efficiency between two temperatures and calculates the full energy balance: Qin, W and Qout. It allows you to quickly assess how much work can be obtained from a given heat source, how temperatures limit efficiency, and how close to the Carnot limit the actual installation can come. It is a useful reference point for selecting exchangers, turbines, condensers and cooling systems, and as teaching material for understanding the limits of energy conversion.